DSU (並查集)
(library/data-structure/dsu.hpp)

• View this file on GitHub
• Last update: 2023-07-30 19:34:47+08:00
• Include: #include "library/data-structure/dsu.hpp"

使用方法

int n;
DSU d(n); // 只有路徑壓縮
DSU<true> d2(n); // 啟發式合併 + 路徑壓縮

int u, v;

int x = d.leader(u);
int sz = d.size(u);
bool success = d.merge(u, v);
bool is_same = d.same(u, v);
vector<vector<int>> g = d.groups();

References

1. AtCoder Library document

Verified with

• test/data-structure/dsu/aoj-dsl-Disjoint-Set-Union-Find-Tree.test.cpp
• test/data-structure/dsu/yosupo-Unionfind.test.cpp

Code

#pragma once
#include <vector>
#include <cassert>
#include <algorithm>

namespace felix {

template<bool UNION_BY_SIZE = false>
struct dsu {
public:
	dsu() : dsu(0) {}
	explicit dsu(int _n) : n(_n), sz(n, -1) {}
	
	int leader(int u) {
		assert(0 <= u && u < n);
		return (sz[u] < 0 ? u : (sz[u] = leader(sz[u])));
	}
	
	bool merge(int a, int b) {
		a = leader(a), b = leader(b);
		if(a == b) {
			return false;
		}
		if constexpr(UNION_BY_SIZE) {
			if(-sz[a] < -sz[b]) {
				std::swap(a, b);
			}
		}
		sz[a] += sz[b];
		sz[b] = a;
		return true;
	}
	
	int size(int u) { return -sz[leader(u)]; }
	bool same(int a, int b) { return leader(a) == leader(b); }

	std::vector<std::vector<int>> groups() {
		std::vector<std::vector<int>> result(n);
		for(int i = 0; i < n; i++) {
			result[leader(i)].push_back(i);
		}
		result.erase(std::remove_if(result.begin(), result.end(), [](const std::vector<int>& v) {
			return v.empty();
		}), result.end());
		return result;
	}

private:
	int n;
	std::vector<int> sz;
};

} // namespace felix

#line 2 "library/data-structure/dsu.hpp"
#include <vector>
#include <cassert>
#include <algorithm>

namespace felix {

template<bool UNION_BY_SIZE = false>
struct dsu {
public:
	dsu() : dsu(0) {}
	explicit dsu(int _n) : n(_n), sz(n, -1) {}
	
	int leader(int u) {
		assert(0 <= u && u < n);
		return (sz[u] < 0 ? u : (sz[u] = leader(sz[u])));
	}
	
	bool merge(int a, int b) {
		a = leader(a), b = leader(b);
		if(a == b) {
			return false;
		}
		if constexpr(UNION_BY_SIZE) {
			if(-sz[a] < -sz[b]) {
				std::swap(a, b);
			}
		}
		sz[a] += sz[b];
		sz[b] = a;
		return true;
	}
	
	int size(int u) { return -sz[leader(u)]; }
	bool same(int a, int b) { return leader(a) == leader(b); }

	std::vector<std::vector<int>> groups() {
		std::vector<std::vector<int>> result(n);
		for(int i = 0; i < n; i++) {
			result[leader(i)].push_back(i);
		}
		result.erase(std::remove_if(result.begin(), result.end(), [](const std::vector<int>& v) {
			return v.empty();
		}), result.end());
		return result;
	}

private:
	int n;
	std::vector<int> sz;
};

} // namespace felix

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